A short electric dipole of dipole moment \(\overrightarrow{P}\) is placed at a distance r from the centre of a solid metallic sphere of radiusa (<< r) as shown in the figure. The electric field intensity at the centre of sphere C due to induced charge on the sphere is
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Solution
Electric field at C due to electric dipole
=\(\frac{1}{4\pi \varepsilon _{0}}\frac{2p}{r^{3}}along\, CO\)
Electric field at C due to induced charge must be equal and opposite to electric field due to dipole as net field at C is zero.
Positive and negative point charges of equal magnitude are kept at (0,0,a⁄2) and (0,0,-a⁄2) respectively. The work done by the electric field when another positive point charge is moved from (–a, 0, 0) to (0,a, 0) is
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Solution
The charges make an electric dipole. A and B points lie on the equitorial plane of the dipole. There fore potential at A= potential at B = 0
W = Q (VA – VB) = q × 0 =0
A charge +q is at a distance L/2 above a square of side L.Then what is the flux linked with the surface?
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Solution
Force between two identical charges placed at a distance of r in vacuum is F. Now a slab of dielectric of dielectric contrant 4 is inserted between these two charges. If the thickness of the slab is r/2, then the force between the charges will become
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Solution
The electric dipole is situated is an electric field as shown in fig 1.The dipole and electric field are bothin the plane of the paper. The dipole is rotated about an axis perpendicular to plane of paper passing through A in anticlockwise direction. If the angle of rotation (θ) is measured with respect to the direction of electric field, then the torque (τ) experienced by the dipole for different values of the angle of rotation q will be represented in fig. 2, by
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Solution
τ =pEsin θ, this is given by the second curve.
There exists a non-uniform electric field along x-axis as shown in the figure below. The field increases at a uniformrate along +ve x-axis. A dipole is placed inside the field as shown. Which one of the following is correct for the dipole?
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Solution
The dipole is placed in a non-uniform field, therefore a force as well as a couple acts on it. The force on the negative charge is more (F α E) and is directed along negative x-axis. Thus the dipole moves along negative x-axis and rotates in an anticlockwise direction.
An electric dipole of moment \(\overrightarrow{P}\) is placed in a uniform electric field \(\overrightarrow{E}\) such that \(\overrightarrow{P}\) points along \(\overrightarrow{E}\). If the dipole is slightly rotated about an axis perpendicular to the plane containing \(\overrightarrow{E}\) and \(\overrightarrow{P}\) and passing through the centre of the dipole, the dipole executes simple harmonic motion.Consider I to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation?
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Solution
A and B are two identically spherical charged bodies which repel each other with force F, kept at a finite distance.A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid point of A and B. Find the magnitude of force on C.
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Solution
A soap bubble is given negative charge, its radius will
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Solution
A metallic sphere is placed in a uniform electric field. The line of force follow the path (s) shown in the figure as
